TP($\omega_2$) and the continuum

I think that in all classical models of TP($\omega_2$) we have $2^{\omega_0}=\omega_2$. Is there a known model of TP($\omega_2$) + $2^{\omega_0}>\omega_2$ at all?

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What is $TP(\omega_2)$? –  Andreas Blass Mar 14 '12 at 18:36
It would seem to be the tree property: every $\omega_2$-tree has an $\omega_2$-branch. –  Joel David Hamkins Mar 14 '12 at 22:15
Yes, I meant the tree property, sorry! –  Ajdin Halilovic Mar 15 '12 at 11:36